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Machine and Application Aware Partitioning for Adaptive Mesh Refinement Applications. In: HPDC '17 Proceedings of the 26th International Symposium on High-Performance Parallel and Distributed Computing
Load balancing and partitioning are critical when it comes to parallel computations. Popular partitioning strategies based on space filling curves focus on equally dividing work. The partitions produced are independent of the architecture or the application. Given the ever-increasing relative cost of data movement and increasing heterogeneity of our architectures, it is no longer sufficient to only consider an equal partitioning of work. Minimizing communication costs are equally if not more important. Our hypothesis is that an unequal partitioning that minimizes communication costs significantly can scale and perform better than conventional equal-work partitioning schemes. This tradeoff is dependent on the architecture as well as the application. We validate our hypothesis in the context of a finite-element computation utilizing adaptive mesh-refinement. Our central contribution is a new partitioning scheme that minimizes the overall runtime of subsequent computations by performing architecture and application-aware non-uniform work assignment in order to decrease time to solution, primarily by minimizing data-movement. We evaluate our algorithm by comparing it against standard space-filling curve based partitioning algorithms and observing time-to-solution as well as energy-to-solution for solving Finite Element computations on adaptively refined meshes. We demonstrate excellent scalability of our new partition algorithm up to $262,144$ cores on ORNL's Titan and demonstrate that the proposed partitioning scheme reduces overall energy as well as time-to-solution for application codes by up to 22.0%.
Computational Algorithms for Unit Commitment with AC Power Flows (Final Report)
Security-constrained unit commitment (SCUC) is a key component in power system operations. When AC power flow constraints are considered in the SCUC model (AC-SCUC), the problem becomes extremely difficult due to its discrete and non-convex nature, as described in “Grid Optimization Competition Challenge 3 Problem Formulation (GOCC)”. There are four main challenges: (i) Discrete decisions regarding unit online/offline status and start-up/shut-down procedures for every single unit. The number of discrete decision variables increases considerably when a system integrates multiple generators; (ii) Configuration-based combined-cycle formulations, and multi-commodity models that include ramping products, spin/non-spin products, and regulation up/down products. The combined-cycle units introduce additional discrete decision variables and auxiliary service products further complicate the model by connecting multi-commodity products’ continuous and discrete variables; (iii) SCUC models with AC power flow constraints are far more complex due to massive bilinear terms in the large-scale nonlinear power balance equations. The nonlinear power balance equations are further complicated by the discrete step control variables of shunts; (iv) N − 1 contingency analysis. The size of the model increases linearly with the number of contingencies considered, greatly increasing the size of the optimization model. Accordingly, there is an emergent need to develop a robust algorithm capable of deriving a high-quality solution in a short time and passing through contingency tests simultaneously. In this project, we explore innovative techniques to address this challenging problem by integrating advanced polyhedral theory, approximation methods, relaxation strategies, decomposition techniques, and parallel computing. Each technique approaches the problem from a different perspective, leveraging its specific strengths to tackle distinct challenges. Each individual method has demonstrated its effectiveness in the PI’s previous research. Their integration is expected to significantly reduce the computational time required to solve the proposed complex problem. Successful completion of this project has the potential to transform the industry by enhancing optimization solvers capable of handling large-scale day-ahead energy market clearing models within strict time constraints, while incorporating AC power flow constraints. This advancement will lead to reduced overall generation costs and, consequently, increased social welfare.
Entanglement-enhanced ac magnetometry in the presence of Markovian noise
Entanglement is a resource to improve the sensitivity of quantum sensors. In an ideal case, using an entangled state as a probe to detect target fields, we can beat the standard quantum limit by which all classical sensors are bounded. However, since entanglement is fragile against decoherence, it is unclear whether entanglement-enhanced metrology is useful in a noisy environment. Its benefit is indeed limited when estimating the amplitude of dc magnetic fields under the effect of parallel Markovian decoherence, where the noise operator is parallel to the target field. In this paper, on the contrary, we show an advantage to using an entanglement over the classical strategy under the effect of parallel Markovian decoherence when we try to detect ac magnetic fields. We consider a scenario to induce a Rabi oscillation of the qubits with the target ac magnetic fields. Although we can, in principle, estimate the amplitude of the ac magnetic fields from the Rabi oscillation, the signal becomes weak if the qubit frequency is significantly detuned from the frequency of the ac magnetic field. We show that, by using the Greenberger-Horne-Zeilinger (GHZ) states, we can significantly enhance the signal of the detuned Rabi oscillation even under the effect of parallel Markovian decoherence. Further, our method is based on the fact that the interaction time between the GHZ states and ac magnetic fields scales as 1/L to mitigate the decoherence effect, where L is the number of qubits, which contributes to improving the bandwidth of the detectable frequencies of the ac magnetic fields. Our results pave the way for new applications of entanglement-enhanced ac magnetometry.
Robust parallel iterative solvers for linear and least-squares problems (Final Technical Report)
The primary goal of this project is to study and develop robust iterative methods for solving linear systems of equations and least squares systems. The focus of the Minnesota team is on algorithms development, robustness issues, and on tests and validation of the methods on realistic problems. 1. The project begun with an investigation on how to practically update a preconditioner obtained from an ILU-type factorization, when the coefficient matrix changes. 2. We investigated strategies to improve robustness in parallel preconditioners in a specific case of a PDE with discontinuous coefficients. 3. We explored ways to adapt standard preconditioners for solving linear systems arising from the Helmholtz equation. These are often difficult linear systems to solve by iterative methods. 4. We have also worked on purely theoretical issues related to the analysis of Krylov subspace methods for linear systems. 5. We developed an effective strategy for performing ILU factorizations for the case when the matrix is highly indefinite. The strategy uses shifting in some optimal way. The method was extended to the solution of Helmholtz equations by using complex shifts, yielding very good results in many cases. 6. We addressed the difficult problem of preconditioning sparse systems of equations on GPUs. 7. A by-product of the above work is a software package consisting of an iterative solver library for GPUs based on CUDA. This was made publicly available. It was the first such library that offers complete iterative solvers for GPUs. 8. We considered another form of ILU which blends coarsening techniques from Multigrid with algebraic multilevel methods. 9. We have released a new version on our parallel solver - called pARMS [new version is version 3]. As part of this we have tested the code in complex settings - including the solution of Maxwell and Helmholtz equations and for a problem of crystal growth.10. As an application of polynomial preconditioning we considered the problem of evaluating f(A)v which arises in statistical sampling. 11. As an application to the methods we developed, we tackled the problem of computing the diagonal of the inverse of a matrix. This arises in statistical applications as well as in many applications in physics. We explored probing methods as well as domain-decomposition type methods. 12. A collaboration with researchers from Toulouse, France, considered the important problem of computing the Schur complement in a domain-decomposition approach. 13. We explored new ways of preconditioning linear systems, based on low-rank approximations.
PARALLEL PERTURBATION MODEL FOR CYCLE TO CYCLE VARIABILITY PPM4CCV
This code consists of a Fortran 90 implementation of the parallel perturbation model to compute cyclic variability in spark ignition (SI) engines. Cycle-to-cycle variability (CCV) is known to be detrimental to SI engine operation resulting in partial burn and knock, and result in an overall reduction in the reliability of the engine. Numerical prediction of cycle-to-cycle variability (CCV) in SI engines is extremely challenging for two key reasons: (i) high-fidelity methods such as large eddy simulation (LES) are required to accurately capture the in-cylinder turbulent flow field, and (ii) CCV is experienced over long timescales and hence the simulations need to be performed for hundreds of consecutive cycles. In the new technique, the strategy is to perform multiple parallel simulations, each of which encompasses 2-3 cycles, by effectively perturbing the simulation parameters such as the initial and boundary conditions. The PPM4CCV code is a pre-processing code and can be coupled with any engine CFD code. PPM4CCV was coupled with Converge CFD code and a 10-time speedup was demonstrated over the conventional multi-cycle LES in predicting the CCV for a motored engine. Recently, the model is also being applied to fired engines including port fuel injected (PFI) and direct injection spark ignition engines and the preliminary results are very encouraging.
FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica
Numerical simulations of Greenland and Antarctic ice sheets involve the solution of large-scale highly nonlinear systems of equations on complex shallow geometries. This work is concerned with the construction of Schwarz preconditioners for the solution of the associated tangent problems, which are challenging for solvers mainly because of the strong anisotropy of the meshes and wildly changing boundary conditions that can lead to poorly constrained problems on large portions of the domain. In this study, two-level generalized Dryja--Smith--Widlund (GDSW)--type Schwarz preconditioners are applied to different land ice problems, i.e., a velocity problem, a temperature problem, as well as the coupling of the former two problems. We employ the message passing interface (MPI)--parallel implementation of multilevel Schwarz preconditioners provided by the package FROSch (fast and robust Schwarz) from the Trilinos library. The strength of the proposed preconditioner is that it yields out-of-the-box scalable and robust preconditioners for the single physics problems. To the best of our knowledge, this is the first time two-level Schwarz preconditioners have been applied to the ice sheet problem and a scalable preconditioner has been used for the coupled problem. The preconditioner for the coupled problem differs from previous monolithic GDSW preconditioners in the sense that decoupled extension operators are used to compute the values in the interior of the subdomains. Additionally, several approaches for improving the performance, such as reuse strategies and shared memory OpenMP parallelization, are explored. In our numerical study we target both uniform meshes of varying resolution for the Antarctic ice sheet as well as nonuniform meshes for the Greenland ice sheet. We present several weak and strong scaling studies confirming the robustness of the approach and the parallel scalability of the FROSch implementation. Among the highlights of the numerical results are a weak scaling study for up to 32,K processor cores (8,K MPI ranks and 4 OpenMP threads) and 566,M degrees of freedom for the velocity problem as well as a strong scaling study for up to 4,K processor cores (and MPI ranks) and 68,M degrees of freedom for the coupled problem.
FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica
Numerical simulations of Greenland and Antarctic ice sheets involve the solution of large-scale highly nonlinear systems of equations on complex shallow geometries. This work is concerned with the construction of Schwarz preconditioners for the solution of the associated tangent problems, which are challenging for solvers mainly because of the strong anisotropy of the meshes and wildly changing boundary conditions that can lead to poorly constrained problems on large portions of the domain. Here, two-level GDSW (Generalized Dryja–Smith–Widlund) type Schwarz preconditioners are applied to different land ice problems, i.e., a velocity problem, a temperature problem, as well as the coupling of the former two problems. We employ the MPI-parallel implementation of multi-level Schwarz preconditioners provided by the package FROSch (Fast and Robust Schwarz)from the Trilinos library. The strength of the proposed preconditioner is that it yields out-of-the-box scalable and robust preconditioners for the single physics problems. To our knowledge, this is the first time two-level Schwarz preconditioners are applied to the ice sheet problem and a scalable preconditioner has been used for the coupled problem. The pre-conditioner for the coupled problem differs from previous monolithic GDSW preconditioners in the sense that decoupled extension operators are used to compute the values in the interior of the sub-domains. Several approaches for improving the performance, such as reuse strategies and shared memory OpenMP parallelization, are explored as well. In our numerical study we target both uniform meshes of varying resolution for the Antarctic ice sheet as well as non uniform meshes for the Greenland ice sheet are considered. We present several weak and strong scaling studies confirming the robustness of the approach and the parallel scalability of the FROSch implementation. Among the highlights of the numerical results are a weak scaling study for up to 32 K processor cores (8 K MPI-ranks and 4 OpenMP threads) and 566 M degrees of freedom for the velocity problem as well as a strong scaling study for up to 4 K processor cores (and MPI-ranks) and 68 M degrees of freedom for the coupled problem.
Parallel Implementation of Nonadditive Gaussian Process Potentials for Monte Carlo Simulations
A strategy is presented to implement Gaussian process potentials in molecular simulations through parallel programming. Attention is focused on the three-body nonadditive energy, though all algorithms extend straightforwardly to the additive energy. The method to distribute pairs and triplets between processes is general to all potentials. Results are presented for a simulation box of argon, including full box and atom displacement calculations, which are relevant to Monte Carlo simulation. Data on speed-up are presented for up to 120 processes across four nodes. A 4-fold speed-up is observed over five processes, extending to 20-fold over 40 processes and 30-fold over 120 processes.
Fully depleted CMOS pixel sensor development and potential applications
CMOS pixel sensors are often opposed to hybrid pixel sensors due to their very different sensitive layer. In standard CMOS imaging processes, a thin (about 20 μm) low resistivity epitaxial layer acts as the sensitive volume and charge collection is mostly driven by thermal agitation. In contrast, the so-called hybrid pixel technology exploits a thick (typically 300 μm) silicon sensor with high resistivity allowing for the depletion of this volume, hence charges drift toward collecting electrodes. But this difference is fading away with the recent availability of some CMOS imaging processes based on a relatively thick (about 50 μm) high resistivity epitaxial layer which allows for full depletion. This evolution extents the range of applications for CMOS pixel sensors where their known assets, high sensitivity and granularity combined with embedded signal treatment, could potentially foster breakthrough in detection performances for specific scientific instruments. One such domain is the Xray detection for soft energies, typically below 10 keV, where the thin sensitive layer was previously severely impeding CMOS sensor usage. Another application becoming realistic for CMOS sensors, is the detection in environment with a high fluence of non-ionizing radiation, such as hadron colliders. However, when considering highly demanding applications, it is still to be proven that micro-circuits required to uniformly deplete the sensor at the pixel level, do not mitigate the sensitivity and efficiency required. Prototype sensors in two different technologies with resistivity higher than 1 kΩ, sensitive layer between 40 and 50 μm and featuring pixel pitch in the range 25 to 50 μm, have been designed and fabricated. Various biasing architectures were adopted to reach full depletion with only a few volts. Laboratory investigations with three types of sources (X-rays, β-rays and infrared light) demonstrated the validity of the approach with respect to depletion, keeping a low noise figure. Especially, an energy resolution of about 400 eV for 5 keV X-rays was obtained for single pixels. The prototypes have then been exposed to gradually increased fluences of neutrons, from 10{sup 13} to 5x10{sup 14} neq/cm{sup 2}. Again laboratory tests allowed to evaluate the signal over noise persistence on the different pixels implemented. Currently our development mostly targets the detection of soft X-rays, with the ambition to develop a pixel sensor matching counting rates as affordable with hybrid pixel sensors, but with an extended sensitivity to low energy and finer pixel about 25 x 25 μm{sup 2}. The original readout architecture proposed relies on a two tiers chip. The first tier consists of a sensor with a modest dynamic in order to insure low noise performances required by sensitivity. The interconnected second tier chip enhances the read-out speed by introducing massive parallelization. Performances reachable with this strategy combining counting and integration will be detailed. (authors)
CTF Parallel Performance Improvements
CTF is a modernized version of COBRA-TF (Coolant Boiling in Rod Arrays-Two Fluid), which is a thermal hydraulic (T/H) sub-channel code based on a two-phase, two-fluid model that formulates the conservation equations of mass, energy, and momentum for three fields of vapor, continuous liquid, and entrained liquid droplets. Under the Consortium for Advanced Simulation of Light Water Reactors (CASL) program sponsored by the U.S. Department of Energy, CTF is being further developed and improved for modeling and simulation of light water reactors. The code improvements for predicting T/H responses of pressurized water reactor (PWR) cores are focused on its applications to specific challenge problems deemed significant to the industry, such as departure from nucleate boiling (DNB) and crud-induced power shift. The code is also being used for T/H feedback in normal operating condition depletions in PWR and boiling water reactor designs in the reactor core simulator, Virtual Environment for Reactor Applications Core Simulator (VERA-CS), being developed by CASL. CTF modifications under the CASL program include software optimization, new closure models, and parallelization for modeling full reactor core T/H responses. The purpose of this work was to improve the parallel performance of CTF. CTF was originally parallelized via a domain-decomposition strategy using the Message Passing Interface (MPI), in which the basis of a solution domain was a physical assembly in the model. In other words, a user who wanted to perform a parallel solution with CTF had to provide the code one processor per assembly in the model (e.g., 56 cores for a 56 assembly quarter-core model, or 193 cores for a 193 assembly full-core model). This design was rigid, demanding a very specific number of processors for a model; furthermore, when CTF was run in VERA-CS-which typically uses thousands of processors- many processors sat idle during the CTF solve because CTF was unable to use any more processors than there are physical assemblies. This was not necessarily a problem if the CTF execution speed was very fast, but the average time spent in a CTF solve for prototypical PWR operating conditions was significant (i.e., over 20 % of the simulation wall time was being spent in CTF for a standard core depletion simulation). Larger, more computationally intensive simulations performed in support of the CASL DNB challenge problem demonstrated a need for improvements in this original parallelization approach. The specific goal of this work was to allow CTF to use more processors than there are physical assemblies in the model, which would not only speed up CTF and improve the overall efficiency of VERA-CS but also give users more-flexible options for executing their simulations. (authors)
Energy-Efficient Cruise Control Using Optimal Control for a Hybrid Electric Vehicle
Increasing connectivity in passenger vehicles provides for a large amount of look-ahead information about driving conditions. An intelligent control algorithm is presented that takes advantage of this information to obtain the operation strategy for the powertrain of a parallel hybrid electric vehicle, in an uncongested highway cruising situation. In order to guarantee sufficient computational efficiency to meet future online requirements, the algorithm is based on Pontryagin’s Minimum Principle. The whole driving/operation strategy is composed of a series of solutions to the optimal control sub-problem for each separate route segment. The control sequence computed offline is then evaluated in Autonomie. The simulation result shows 6% fuel savings compared to a baseline rule-based controller with no speed optimization.
Accelerating DCA++ (Dynamical Cluster Approximation) Scientific Application on the Summit supercomputer
Optimizing scientific applications on today’s accelerator-based high performance computing systems can be challenging, especially when multiple GPUs and CPUs with heterogeneous memories and persistent non-volatile memories are present. An example is Summit, an accelerator-based system at the Oak Ridge Leadership Computing Facility (OLCF) that is rated as the world’s fastest supercomputer to-date. New strategies are thus needed to expose the parallelism in legacy applications, while being amenable to efficient mapping to the underlying architecture.In this paper we discuss our experiences and strategies to port a scientific application, DCA++, to Summit. DCA++ is a highperformance research application that solves quantum manybody problems with a cutting edge quantum cluster algorithm, the dynamical cluster approximation.Our strategies aim to synergize the strengths of the different programming models in the code. These include: (a) streamlining the interactions between the CPU threads and the GPUs, (b) implementing computing kernels on the GPUs and decreasing CPU-GPU memory transfers, (c) allowing asynchronous GPU communications, and (d) increasing compute intensity by combining linear algebraic operations.Full-scale production runs using all 4600 Summit nodes attained a peak performance of 73.5 PFLOPS with a mixed precision implementation.We observed a perfect strong and weak scaling for the quantum Monte Carlo solver in DCA++, while encountering about 2× input/output (I/O) and MPI communication overhead on the time-to-solution for the full machine run. Our hardware agnostic optimizations are designed to alleviate the communication and I/O challenges observed, while improving the compute intensity and obtaining optimal performance on a complex, hybrid architecture like Summit.
Parallelized POD-based suboptimal economic model predictive control of a state-constrained Boussinesq approximation
Motivated by an energy efficient building application, we want to optimize a quadratic cost functional subject to the Boussinesq approximation of the Navier-Stokes equations and to bilateral state and control constraints. Since the computation of such an optimal solution is numerically costly, we design an efficient strategy to compute a sub-optimal (but applicationally acceptable) solution with significantly reduced computational effort. We employ an economic Model Predictive Control (MPC) strategy to obtain a feedback control. The MPC sub-problems are based on a linear-quadratic optimal control problem subjected to mixed control and state constraints and a convection-diffusion equation, reduced with proper orthogonal decomposition. Finally, to solve each sub-problem, we apply a primal-dual active set strategy. The method can be fully parallelized, which enables the solution of large problems with real-world parameters.
2.2.3.106 - Lignin-First Biorefinery Development
The Lignin-First Biorefinery Development (LigFirst) project aims to develop a cost-effective, and scalable biomass fractionation strategy based on reductive catalytic fractionation (RCF). The RCF process uses a protic solvent, hydrogen gas or a hydrogen donor, and a metal catalyst in the presence of intact biomass to produce a stable, depolymerized lignin oil and a polysaccharide pulp, which can both be converted to value-added products in parallel processes. RCF is a promising strategy to enable the use of woody feedstocks in biochemical conversion processes and is also promising as a means to valorize lignin with equal emphasis to biomass carbohydrates. Guided by techno-economic analysis and life cycle assessment and in collaboration with industry partners, we are actively developing RCF methods to 1) avoid the need for exogenous hydrogen gas, 2) substantially reduce reactor pressure via use of low vapor pressure solvents, 3) separate the lignin solvolysis and catalytic processes through reaction engineering solutions, 4) reduce solvent loading below what can be achieved in typical batch reactors, and 5) avoid or minimize the use of organic solvents. The LigFirst project also collaborates closely with the Lignin Utilization and Lignin Conversion-to-SAF projects for critical substrate handoffs and analytics. Overall, the LigFirst project is enabling new approaches that ultimately can enable RCF to be a feedstock-agnostic method to valorize both polysaccharides and lignin.
Design Considerations for GPU-based Mixed Integer Programming on Parallel Computing Platforms
Mixed Integer Programming (MIP) is a powerful abstraction in combinatorial optimization that finds real-life application across many significant sectors. The recent proliferation of graphical processing unit (GPU)-based accelerated computing architectures in large-scale parallel computing or supercomputing presents new opportunities as well as challenges in the advancement of MIP solver technology to effectively use the new accelerated computing platforms and scale to large parallel systems. Here, we recount the conventional processor-based strategies and focus on configurations where the most promising intersection lies between parallel MIP solver approaches and the specific strengths of accelerated parallel platforms. We note that the best potential lies in solving problems whose individual matrix sizes (of the linear program relaxation) fit entirely within one accelerator's memory and whose branch-and-bound (or branch-and-cut) trees cannot be fully contained within a small number of computational nodes. Additionally, we identify ideal features of computational linear algebra support on GPU accelerators that would help advance this direction of scalable parallel solution of MIP problems on GPU-based accelerated computing architectures.
Stochastic optimization of GeantV code by use of genetic algorithms
GeantV is a complex system based on the interaction of different modules needed for detector simulation, which include transport of particles in fields, physics models simulating their interactions with matter and a geometrical modeler library for describing the detector and locating the particles and computing the path length to the current volume boundary. The GeantV project is recasting the classical simulation approach to get maximum benefit from SIMD/MIMD computational architectures and highly massive parallel systems. This involves finding the appropriate balance between several aspects influencing computational performance (floating-point performance, usage of off-chip memory bandwidth, specification of cache hierarchy, etc.) and handling a large number of program parameters that have to be optimized to achieve the best simulation throughput. This optimization task can be treated as a black-box optimization problem, which requires searching the optimum set of parameters using only point-wise function evaluations. Here, the goal of this study is to provide a mechanism for optimizing complex systems (high energy physics particle transport simulations) with the help of genetic algorithms and evolution strategies as tuning procedures for massive parallel simulations. One of the described approaches is based on introducing a specific multivariate analysis operator that could be used in case of resource expensive or time consuming evaluations of fitness functions, in order to speed-up the convergence of the black-box optimization problem.
Numerical Prediction of CCV in a PFI Engine using a Parallel LES Approach
Cycle-to-cycle variability (CCV) is detrimental to IC engine operation and can lead to partial burn, misfire, and knock. Predicting CCV numerically is extremely challenging due to two key reasons. Firstly, high-fidelity methods such as large eddy simulation (LES) are required to accurately resolve the incylinder turbulent flowfield both spatially and temporally. Secondly, CCV is experienced over long timescales and hence the simulations need to be performed for hundreds of consecutive cycles. Ameen et al. (Int. J. Eng. Res., 2017) developed a parallel perturbation model (PPM) approach to dissociate this long time-scale problem into several shorter timescale problems. The strategy is to perform multiple single-cycle simulations in parallel by effectively perturbing the initial velocity field based on the intensity of the in-cylinder turbulence. This strategy was demonstrated for motored engine and it was shown that the mean and variance of the in-cylinder flowfield was captured reasonably well by this approach. In the present study, this PPM approach is extended to simulate the CCV in a fired port-fuel injected (PFI) SI engine. Two operating conditions are considered – a medium CCV operating case corresponding to 2500 rpm and 16 bar BMEP and a low CCV case corresponding to 4000 rpm and 12 bar BMEP. The predictions from this approach are also shown to be similar to the consecutive LES cycles. Both the consecutive and PPM LES cycles are observed to under-predict the variability in the early stage of combustion. The parallel approach slightly underpredicts the cyclic variability at all stages of combustion as compared to the consecutive LES cycles. However, it is shown that the parallel approach is able to predict the coefficient of variation (COV) of the in-cylinder pressure and burn rate related parameters with sufficient accuracy, and is also able to predict the qualitative trends in CCV with changing operating conditions. The convergence of the statistics predicted by the PPM approach with respect to the number of consecutive cycles required for each parallel simulation is also investigated. It is shown that this new approach is able to give accurate predictions of the CCV in fired engines in less than one-tenth of the time required for the conventional approach of simulating consecutive engine cycles.